A capacitor is half filled with a dielectric $(K=2)$ as shown in figure A. If the same capacitor is to be filled with same dielectric as shown, what would be the thickness of dielectric so that capacitor still has same capacity?
Medium
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(a)
$C_{\text {net }}=\frac{k+1}{2} \frac{A \varepsilon_0}{d}$
$C_{\text {net }}=\frac{A \varepsilon_0}{d-t\left(1-\frac{1}{2}\right)}=\frac{A \varepsilon_0}{d-\frac{t}{2}}$
$C_{\text {net }}=\frac{3 A \varepsilon_0}{2 d}$
$\frac{3 A \varepsilon_0}{2 d}=\frac{A \varepsilon_0}{d-\frac{t}{2}}$
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